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0580/31 Oct/Nov 2022, Question 8: Adding and Subtracting Vectors

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 10 marks

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The question, in short

Work with column vectors a = (−3, 5) and b = (7, −4), and use coordinate grids to find points, plot points, draw a line, and find equations of lines.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Calculate 4a for the column vector a = (−3, 5).

  1. 14a = 4 × column vector (−3, 5) = column vector (−12, 20)

Answercolumn vector (−12, 20)

Part (aii) · 2 marks

Calculate 2a − b for a = (−3, 5) and b = (7, −4).

  1. 12a = column vector (−6, 10)
  2. 22a − b = column vector (−6 − 7, 10 − (−4)) = column vector (−13, 14)

Answercolumn vector (−13, 14)

Part (bi) · 1 mark

Write down the coordinates of point P marked on the grid.

  1. 1P is 3 right and 1 up: (3, 1)

Answer(3, 1)

Part (bii) · 1 mark

Plot point Q at (−4, 2) on the grid.

  1. 1Go 4 left and 2 up from the origin and mark Q at (−4, 2)

AnswerQ plotted at (−4, 2)

Part (biii) · 1 mark

Given vector PR = (−2, 1), plot point R on the grid.

  1. 1R = (3 − 2, 1 + 1) = (1, 2)
  2. 2Plot R at (1, 2)

AnswerR plotted at (1, 2)

Part (biv) · 1 mark

Draw the line y = 3 on the grid.

  1. 1Draw a horizontal ruled line through y = 3 across the grid

AnswerLine y = 3 drawn

Part (ci) · 2 marks

Find the equation of line L shown on the grid in the form y = mx + c.

  1. 1L crosses the y-axis at (0, −3), so c = −3
  2. 2From (0, −3) to (1, −1): gradient = 2 ÷ 1 = 2
  3. 3y = 2x − 3

Answer2x − 3

Part (cii) · 1 mark

Write down the equation of any line parallel to line L.

  1. 1Parallel lines have the same gradient 2
  2. 2e.g. y = 2x + 1 (any y = 2x + k with k ≠ −3)

Answer2x + k

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Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 8.
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